Let \( f: N \rightarrow R \) and \( g: N \rightarrow R \) be two functions and \( f(1)=0.8, g(1)...

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Let \( f: N \rightarrow R \) and \( g: N \rightarrow R \) be two functions and \( f(1)=0.8, g(1)=0.6 ; f(n+1)=f(n) \cos (g(n))-g(n) \sin (g(n)) \) and \( g(n+1)=f(n) \sin (g(n))+g(n) \cos (g(n)) \) for \( n \geq 1 \).
\( \lim _{n \rightarrow \infty} g(n) \) is equal to
(a) \( -1 \)
(b) 0
(c) 1
(d) does not exist
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